The star was not overwhelmingly strong.
In the JPEG files I pulled from the movie,
each pixel can have a value between 0 and 255 counts.
The typical background near the star was around 40 counts.
The star itself was not saturated, having a peak value
around 120 counts.
The FWHM of the stellar image was around 3 pixels.
I estimate very roughly from the size of the
Moon in the images that
each pixel is about 5 arcsec on a side.

For each of the 7199 frames, I

tried to find the star,
using a small box around its rough location.
To help, I convolved the image in this box with a
2-D circular gaussian with FWHM 4 pixels

if I found the star, I noted its position;
if not, I used the most recent detected position

placed a circular aperture of radius
3 pixels (see below) around this position

added up all the light within this aperture

calculated a sky value based on pixels
in an annulus of inner radius 8 pixels,
outer radius 15 pixels

subtracted the contribution of the background
sky to the light within the aperture

There was a complication:
in many images, the star itself was invisible,
yet my software claimed to find an "object".
These were noise peaks, I suppose.
It is clear that there are a significant number of such
false detections if one looks at the location
of the "object" in all frames.
In the graph below, I place a red dot at
the (row, col) position of the detected "object" in all frames.

As you can see, the field of view drifted slightly over
the course of the 4-minute video record.
The real detections define a snake-like locus,
with a big break where there was a prolonged
disappearance.
The individual points located far from this locus
are false detections.
To get rid of many (but not all) of them,
I drew two lines, shown in the diagram above,
and discarded any detection outside the lines.

I also found that the detections after frame
7100 were noisy, so I discarded them, too.
That left me with 5219 measurements,
most of which were either real detections
or at least measurements at the proper location.

The photometry taken at the positions of these false detections
gave me a useful bit of information:
it showed the amount of light above background
that an aperture placed on a random location would yield.

In short, the precision of the photometry is pretty low:
around 20 percent.
Note that the V-band magnitude for
85 Ceti is about
V = 6.3;
it is marked in
SIMBAD
as a variable star, however, and I don't know
what its magnitude was exactly at the time of the
occultation.

Here are quick views of the results.
I have placed a dotted green line at the
level of false detections, to indicate a reasonable
limit for trusting the measurements.

The entire light curve:

A closeup around the first brief disappearance:

A closeup around the second, prolonged disappearance:

A closeup around frames 3300 to 4200:

A closeup around frames 4000 to 5200:

A closeup around frames 5000 to 5800:

You can grab the data in a multi-column ASCII text file below.
The columns are